FEMA Improvement, Reform, and Efficiency Act of 2021 or the FIRE Act This bill addresses the federal government's approach to wildfires. Specifically, the bill authorizes an eligible applicant seeking public mitigation assistance to relocate an eligible structure upon demonstrating that the structure is at risk from future damage and the relocation reduces the risk to the structure and does not increase risk to adjacent structures. The Federal Emergency Management Agency (FEMA), in coordination with the National Weather Service, must conduct a study on Red Flag Warnings and similar weather alert and notification methods to implement plans and actions prior to a wildfire event that can limit the impact, duration, or severity of the fire. The Government Accountability Office must report to Congress regarding wildfires, including the effectiveness of FEMA programs in addressing wildfires and other hazards. The President must ensure that those providing case management services to victims of a major disaster have cultural competency training. FEMA must (1) conduct a study and develop a plan to address providing housing assistance to survivors of major disasters or emergencies when presented with challenges such as the lack of proof of ownership or ownership documentation, and (2) seek to contract with the National Academy of Sciences to study potential solutions to address the availability and affordability of insurance for wildfire perils and other related matters. The bill allows Indian tribal governments to apply for grants for equipping, upgrading, and constructing state and local emergency operations centers.